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Number and Algebra

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Number sets and properties (Natural, Integers, Rational, Real)

Subtopic

Number sets and properties (Natural, Integers, Rational, Real) under Number and Algebra for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If a number is denoted as x∈Z+x \in \mathbb{Z}^+, what does this mean?

    A.

    xx is a negative integer

    B.

    xx is a positive integer

    C.

    xx is any rational number

    D.

    xx is zero

  2. 2.

    Which of these decimals is the same as 1/21/2?

    A.

    0.050.05

    B.

    0.50.5

    C.

    0.20.2

    D.

    0.120.12

  3. 3.

    Evaluate ∣−3×4∣|-3 \times 4|.

    A.

    −12-12

    B.

    1212

    C.

    77

    D.

    −7-7

Download the worksheet for Number and Algebra - Number sets and properties (Natural, Integers, Rational, Real) to practice offline. It includes additional chapter-level practice questions.

Laws of exponents and radicals

Subtopic

Laws of exponents and radicals under Number and Algebra for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Simplify the expression p2p9\frac{p^2}{p^9}.

    A.

    p7p^7

    B.

    p−7p^{-7}

    C.

    p11p^{11}

    D.

    1p−7\frac{1}{p^{-7}}

  2. 2.

    Simplify the expression (5x3)2(5x^3)^2.

    A.

    10x610x^6

    B.

    25x625x^6

    C.

    25x525x^5

    D.

    10x510x^5

  3. 3.

    Evaluate the expression 144/169\sqrt{144/169}.

    A.

    12/1312/13

    B.

    14/1614/16

    C.

    12/16912/169

    D.

    144/13144/13

Download the worksheet for Number and Algebra - Laws of exponents and radicals to practice offline. It includes additional chapter-level practice questions.

Logarithms and their properties

Subtopic

Logarithms and their properties under Number and Algebra for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Express log⁡xy2\log_x y^2 using the power rule.

    A.

    (log⁡xy)2(\log_x y)^2

    B.

    2log⁡xy2 \log_x y

    C.

    log⁡x(2y)\log_x (2y)

    D.

    12log⁡xy\frac{1}{2} \log_x y

  2. 2.

    Evaluate log⁡2(2×4)\log_2 (2 \times 4).

    A.

    8

    B.

    3

    C.

    2

    D.

    6

  3. 3.

    Solve for xx: log⁡10x=−2\log_{10} x = -2.

    A.

    -20

    B.

    0.01

    C.

    0.02

    D.

    -100

Download the worksheet for Number and Algebra - Logarithms and their properties to practice offline. It includes additional chapter-level practice questions.

Arithmetic and Geometric sequences and series

Subtopic

Arithmetic and Geometric sequences and series under Number and Algebra for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Which of these is the correct formula for the sum of the first nn terms of a geometric series?

    A.

    Sn=u1(rn−1)r−1S_n = \frac{u_1(r^n - 1)}{r - 1}

    B.

    Sn=n2(2u1+d)S_n = \frac{n}{2}(2u_1 + d)

    C.

    Sn=u1+rn−1S_n = u_1 + r^{n-1}

    D.

    Sn=u1+(n−1)dS_n = u_1 + (n-1)d

  2. 2.

    What is the 20th20^{th} term of an arithmetic sequence where u1=5u_1 = 5 and d=0d = 0?

    A.

    00

    B.

    55

    C.

    2020

    D.

    2525

  3. 3.

    Find the 3rd3^{rd} term of the geometric sequence 1,12,…1, \frac{1}{2}, \dots.

    A.

    13\frac{1}{3}

    B.

    14\frac{1}{4}

    C.

    16\frac{1}{6}

    D.

    00

Download the worksheet for Number and Algebra - Arithmetic and Geometric sequences and series to practice offline. It includes additional chapter-level practice questions.

Algebraic manipulation (expansion, factorization)

Subtopic

Algebraic manipulation (expansion, factorization) under Number and Algebra for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Factorize the trinomial x2+13x+42x^2 + 13x + 42.

    A.

    (x+1)(x+42)(x + 1)(x + 42)

    B.

    (x+2)(x+21)(x + 2)(x + 21)

    C.

    (x+6)(x+7)(x + 6)(x + 7)

    D.

    (x+3)(x+14)(x + 3)(x + 14)

  2. 2.

    Expand and simplify (x−6)(x−2)(x - 6)(x - 2).

    A.

    x2+8x+12x^2 + 8x + 12

    B.

    x2−8x+12x^2 - 8x + 12

    C.

    x2−8x−12x^2 - 8x - 12

    D.

    x2−4x+12x^2 - 4x + 12

  3. 3.

    Factorize 16x2−2516x^2 - 25.

    A.

    (4x−5)2(4x - 5)^2

    B.

    (8x−5)(8x+5)(8x - 5)(8x + 5)

    C.

    (4x−5)(4x+5)(4x - 5)(4x + 5)

    D.

    (16x−25)(x+1)(16x - 25)(x + 1)

Download the worksheet for Number and Algebra - Algebraic manipulation (expansion, factorization) to practice offline. It includes additional chapter-level practice questions.

Solving linear, quadratic, and simultaneous equations

Subtopic

Solving linear, quadratic, and simultaneous equations under Number and Algebra for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Solve for xx: 2x−10=02x - 10 = 0.

    A.

    x=−5x = -5

    B.

    x=2x = 2

    C.

    x=10x = 10

    D.

    x=5x = 5

  2. 2.

    Find xx if x2=1x^2 = 1.

    A.

    x=1x = 1 or x=−1x = -1

    B.

    x=0x = 0

    C.

    x=1x = 1

    D.

    x=−1x = -1

  3. 3.

    Solve the system: x+y=8x + y = 8 and x−y=8x - y = 8.

    A.

    x=8,y=0x = 8, y = 0

    B.

    x=0,y=8x = 0, y = 8

    C.

    x=4,y=4x = 4, y = 4

    D.

    x=16,y=−8x = 16, y = -8

Download the worksheet for Number and Algebra - Solving linear, quadratic, and simultaneous equations to practice offline. It includes additional chapter-level practice questions.

Binomial theorem (introduction)

Subtopic

Binomial theorem (introduction) under Number and Algebra for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    How many terms are there in the expansion of (x+y)0(x + y)^{0}?

    A.

    00

    B.

    11

    C.

    22

    D.

    Undefined

  2. 2.

    What is the coefficient of the a4a^{4} term in the expansion of (a+b)4(a + b)^{4}?

    A.

    11

    B.

    44

    C.

    66

    D.

    1212

  3. 3.

    Calculate the sum (20)+(21)+(22)\binom{2}{0} + \binom{2}{1} + \binom{2}{2}.

    A.

    22

    B.

    33

    C.

    44

    D.

    55

Download the worksheet for Number and Algebra - Binomial theorem (introduction) to practice offline. It includes additional chapter-level practice questions.

Number and Algebra - IB Grade 10 Maths Notes & Revision | Krit.club